Infrared light is widely used in machine tools such as CO.sub.2 laser welder or cutting machine, or in measuring instruments such as spectral analyzer or IR thermometer. Flexible optical fibers are used as an infrared light guide, and they are advantageous in that they can transmit light along a desired path. The fibers currently employed for optical communication are made of quartz glass and other oxide glass, but they cannot be used for transmitting infrared light because they have great transmission loss. Attempts have been made to produce a polycrystalline fiber by hot-extruding thallium halide such as KRS-5 [TlBr (45.7 mol%)-TlI (54.3 mol%)] or a silver halide such as silver chloride or silver bromide. In another attempt, a fiber is produced by growing a molten salt of KRS-5 or silver bromide into a single crystal having a diameter of 0.4 to 1 mm. The fiber obtained is loosely fitted into a Teflon or other resin pipe and used as a structure wherein the fiber is a core and air is a cladding. With such structure, if an alkali metal halide is used as the infrared light transmitting crystalline material, the fiber absorbs the moisture of the air cladding and often undergoes mechanical or optical deterioration. If the fiber is made of a less hygroscopic but softer thallium halide, silver halide or alkaline earth metal halide, freedom of the movement of the fiber within the pipe causes slip deformation of the halide crystal, and as a result, the optical properties of the surface of the core fiber are impaired by surface roughening or light scattering, and at the same time, the fiber fatigues to increase the chance of deteriorated mechanical properties.
These defects may be eliminated by preparing a fiber having a refractive index distribution to confine the light to be transmitted within the fiber and by reinforcing the fiber with a protective coating that is in close contact with the fiber. But if a fiber consisting of a core of high refractive index and a cladding of low refractive index is produced by hot extrusion, the crystal grains making the core and cladding have a size of from several micrometers to several hundreds of micrometers and an irregular interface is easily formed between the core and cladding. Furthermore, if a crystalline fiber is prepared from molten material, the melting point of the infrared light transmitting crystal serving as the core is generally lower than that of the infrared light transmitting crystal serving as the cladding, and the cladding crystal cannot be grown around the core crystal without melting the latter. It has therefore been difficult to produce a crystalline fiber having the desired refractive index distribution whether it is a polycrystalline or single crystal fiber.